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Items from 1 to 16 out of 16 results

article

Coarser connected topologies

William G. Fleissner, Jack Porter, Judith Roitman

Topology and its Applications > 2004 > 142 > 1-3 > 131-157

We investigate which spaces have coarser connected topologies. If in a collectionwise normal space X, the density equals the extent, which is attained and at least c, then X has a coarser connected collectionwise normal topology. In the previous sentence, the separation property collectionwise normal can be replaced by other separation properties-for example, Hausdorff, Urysohn, regular, metrizable...

article

The homeomorphism problem for countable topological spaces

Su Gao

Topology and its Applications > 2004 > 139 > 1-3 > 97-112

We consider the homeomorphism problem for countable topological spaces and investigate its descriptive complexity as an equivalence relation. It is shown that even for countable metric spaces the homeomorphism problem is strictly more complicated than the isomorphism problem for countable graphs and indeed it is not Borel reducible to any orbit equivalence relation induced by a Borel action of a Polish...

article

Finite intervals in the partial orders of zero-dimensional, Tychonoff and regular topologies

D.W. McIntyre, W.S. Watson

Topology and its Applications > 2004 > 139 > 1-3 > 23-36

For a set X, let Σ _z (X), Σ _t (X) and Σ ₃ (X) denote, respectively, the sets of Hausdorff zero-dimensional, Tychonoff and Hausdorff regular topologies on X, partially ordered by inclusion. We investigate the nature of intervals in these partially ordered sets, with emphasis on finite intervals. We show that all such intervals are lattices, and that basic intervals (i.e., intervals...

article

On a conjecture about spectral sets

Karim Belaid, Othman Echi

Topology and its Applications > 2004 > 139 > 1-3 > 1-15

Let R be a commutative ring with identity. We denote by Spec(R) the set of prime ideals of R. Call a partial ordered set spectral if it is order isomorphic to (Spec(R), ) for some R. A longstanding open question about spectral sets (since 1976), is that of Lewis and Ohm [Canad. J. Math. 28 (1976) 820, Question 3.4]: ''If (X,=<) is an ordered disjoint union of the posets (X _λ ,=< ...

article

Properties related to first countability and countable compactness in hyperspaces: a new approach

G. Di Maio, Ľ. Holá, E. Meccariello

Topology and its Applications > 2004 > 137 > 1-3 > 83-97

We study properties related to first countability and countable compactness of uniformizable Δ-hit-and-miss hyperspace topologies. We show that they are proximal hyperspace topologies. We use the Smirnov compactification as a tool in our investigation.

article

Cocompactness and quasi-uniformizability of completely metrizable spaces

H.-P.A. Künzi

Topology and its Applications > 2003 > 133 > 1 > 89-95

We show that a metrizable topological space X is completely metrizable if and only if it admits a quasi-uniformity U such that the topology induced by the conjugate quasi-uniformity U ^- ¹ on X is compact.

article

H-trivial spaces

A. Bouziad

Topology and its Applications > 2003 > 132 > 2 > 159-174

Let X be a regular Hausdorff space and H a subcollection of the lattice F of all closed subsets of X, which is hereditary with respect to closed sets and stable under finite unions. The space X is called H-trivial if the co-compact topology on H coincides with the corresponding upper Kuratowski topology. We propose a description of H-trivial spaces in terms of open sieves, providing parallels and...

article

Maximal complements in the lattices of pre-orders and topologies

Carlos Uzcátegui

Topology and its Applications > 2003 > 132 > 2 > 147-157

Two topologies τ and ρ over X are said to be complementary if τ ρ is the indiscrete topology and τ ρ the discrete topology. The lattice of topologies is complemented, i.e., every topology has a complement. We will show that every AT topology (i.e., a topology such that the intersection of arbitrary many open sets is open) over a countable set has a maximal complement in the lattice of topologies...

article

Provisional solution to a Comfort-van Mill problem

Michael Tkachenko

Topology and its Applications > 2002 > 125 > 1 > 171-182

We prove under the assumption of Martin's Axiom that an abstract Abelian group G of non-measurable cardinality is the intersection of countably compact subgroups of its Bohr compactification bG. This result is used to show that weakly free countably compact topological groups do not exist, thus answering a question posed by Comfort and van Mill in 1988. In fact, we show under MA that a free (P,CC)-group...

article

Measurable cardinals and finite intervals between regular topologies

C. Good, D.W. McIntyre, W.S. Watson

Topology and its Applications > 2002 > 123 > 3 > 429-441

Assuming the existence of infinitely many measurable cardinals, a finite lattice is isomorphic to the interval between two T ₃ topologies on some set if and only if it is distributive. A characterisation is given for those finite lattices which are isomorphic to the interval between two T ₃ topologies on a countable set.

article

On θ-connectedness and θ-closure spaces

Mila Mršević, Dimitrije Andrijević

Topology and its Applications > 2002 > 123 > 1 > 157-166

Let (X,T) be a topological space. A point x is in the θ-closure of A, denoted by cl _θ A, if each closed neighbourhood of x intersects A. The pair (X,cl _θ ) is a closure space, also called a neighbourhood space. A subset A is θ-closed if A=cl _θ A. θ-closed sets are closed sets for a new topology T _θ on the set X. The semi-regularization topology of T is denoted by T...

article

On compact weaker topologies in function spaces

Fidel Casarrubias-Segura

Topology and its Applications > 2001 > 115 > 3 > 291-298

In this paper we prove that for every cardinal κ, the space C _p (D ^κ ) admits a continuous bijection onto a space whose all finite powers are Lindelof (the symbol D stands for the discrete two-point space). We also prove that for every metrizable compact space X, the space C _p (X) can be condensed (i.e., admits a continuous bijection) onto the Hilbert cube I ^ω . As...

article

Ultrafilter spaces on the semilattice of partitions

Lorenz Halbeisen, Benedikt Löwe

Topology and its Applications > 2001 > 115 > 3 > 317-332

The Stone-Cech compactification of the natural numbers βω (or equivalently, the space of ultrafilters on the subsets of ω) is a well-studied space with interesting properties. Replacing the subsets of ω by partitions of ω in the construction of the ultrafilter space gives non-homeomorphic spaces of partition ultrafilters corresponding to βω. We develop a general framework for spaces of this type and...

article

Analytic topologies over countable sets

Stevo Todorčević, Carlos Uzcátegui

Topology and its Applications > 2001 > 111 > 3 > 299-326

In this article we attempt to a systematic study of analytic topologies over the natural numbers N (or any countable set X).

article

The regular-locally compact coreflection of a stably locally compact locale

Martı́n Hötzel Escardó

Journal of Pure and Applied Algebra > 2001 > 157 > 1 > 41-55

The Scott continuous nuclei form a subframe of the frame of all nuclei. We refer to this subframe as the patch frame. We show that the patch construction exhibits (i) the category of regular locally compact locales and perfect maps as a coreflective subcategory of the category of stably locally compact locales and perfect maps, (ii) the category of compact regular locales and continuous maps as a...

article

Separate versus joint continuity: A tale of four topologies

M. Henriksen, R.G. Woods

Topology and its Applications > 1999 > 97 > 1-2 > 175-205

Several naturally occurring topologies on the product XxY of the Tychonoff spaces X and Y are studied; each is stronger than the product topology τ. These include the cross topology γ consisting of sets meeting each horizontal and vertical fiber in a set open in the subspace topology induced by τ; the weak topology σ determined by the separately continuous real-valued functions with domain XxY; and...

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Keywords

[MATHEMATICAL SUBJECT CODES] 54A10 (16)
COUNTABLE TOPOLOGICAL SPACES (2)
LATTICE OF TOPOLOGIES (2)
[MATHEMATICAL SUBJECT CODES] 06B15 (2)
[MATHEMATICAL SUBJECT CODES] 54A05 (2)
[MATHEMATICAL SUBJECT CODES] 54B10 (2)
[MATHEMATICAL SUBJECT CODES] 54B20 (2)
[MATHEMATICAL SUBJECT CODES] 54D05 (2)
[MATHEMATICAL SUBJECT CODES] 54D15 (2)
[MATHEMATICAL SUBJECT CODES] 54D30 (2)
[MATHEMATICAL SUBJECT CODES] 54H05 (2)
(PROXIMAL) Δ-HIT-AND-MISS HYPERSPACE TOPOLOGY (1)
ABELIAN GROUP (1)
ANALYTIC SETS (1)
BOHR COMPACTIFICATION (1)
BOREL ACTION (1)
BOREL REDUCIBILITY (1)
CHARACTER (1)
CO-COMPACT TOPOLOGY (1)
COARSER CONNECTED TOPOLOGY (1)
COCOMPACT (1)
COMPACT-COVERING MAP (1)
COMPACTNESS (1)
COMPLEMENTED LATICES (1)
COMPLETE REGULARIZATION (1)
COMPLETELY METRIZABLE (1)
CONDENSATION (1)
CONNECTEDNESS (1)
COSUBOBJECTS (1)
COUNTABLY COMPACT (1)
CROSS TOPOLOGY (1)
EMBEDDING (1)
EXTENT (1)
F-SPACES (1)
FIRST COUNTABILITY (1)
FUNCTION SPACES (1)
GRAPH ISOMORPHISM (1)
HYPERSPACE TOPOLOGY (1)
HYPERSPACES (1)
K-SPACE (1)
LATTICES OF TOPOLOGIES AND PARTIAL ORDERS (1)
LOCAL CONNECTEDNESS (1)
MARTIN'S AXIOM (1)
MEASURABLE CARDINAL (1)
METRIZABLE (1)
NEIGHBOURHOOD SPACE (1)
ORDERED DISJOINT UNION (1)
ORDINALS (1)
P-POINTS (1)
P-SPACE (1)
PAIRWISE COMPLETELY REGULAR (1)
PARTITIONS (1)
POLISH GROUP (1)
PRECOMPACT (1)
PROXIMITY (1)
PSEUDOCOMPACT (1)
PSEUDOCOMPACT SPACE (1)
Q-COVERING MAP (1)
QUASI-UNIFORMITY (1)
REALCOMPACT SPACE (1)
SEMI-REGULARIZATION TOPOLOGY (1)
SEPARABILITY (1)
SEPARATELY CONTINUOUS FUNCTIONS (1)
SEPARATION PROPERTIES (1)
SEQUENTIALLY COMPLETE (1)
SHATTERING FAMILIES (1)
SMIRNOV COMPACTIFICATION (1)
SPECTRAL SET (1)
SPECTRAL TOPOLOGY (1)
STONE TOPOLOGIES ON SEMILATTICES (1)
STRONG COUNTABLE COMPACTNESS (1)
SWELLING (1)
TIGHTNESS (1)
TOPOLOGY OF POINTWISE CONVERGENCE (1)
TOPOLOGY OF SEPARATE CONTINUITY (1)
TRI-QUOTIENT MAP (1)
ULTRAFILTER SPACES (1)
UNIFORMITY (1)
UPPER KURATOWSKI CONVERGENCE (1)
URYSOHN SPACE (1)
VARIETY OF TOPOLOGICAL GROUPS (1)
WEAKER TOPOLOGIES (1)
WEAKLY FREE (U,V)-GROUP (1)
[MATHEMATICAL SUBJECT CODES] 03E10 (1)
[MATHEMATICAL SUBJECT CODES] 03E17 (1)
[MATHEMATICAL SUBJECT CODES] 03E35 (1)
[MATHEMATICAL SUBJECT CODES] 04A15 (1)
[MATHEMATICAL SUBJECT CODES] 06A06 (1)
[MATHEMATICAL SUBJECT CODES] 06B30 (1)
[MATHEMATICAL SUBJECT CODES] 06B35 (1)
[MATHEMATICAL SUBJECT CODES] 06C15 (1)
[MATHEMATICAL SUBJECT CODES] 06E15 (1)
[MATHEMATICAL SUBJECT CODES] 22A05 (1)
[MATHEMATICAL SUBJECT CODES] 54A25 (1)
[MATHEMATICAL SUBJECT CODES] 54A35 (1)
[MATHEMATICAL SUBJECT CODES] 54B05 (1)
[MATHEMATICAL SUBJECT CODES] 54C08 (1)
[MATHEMATICAL SUBJECT CODES] 54C10 (1)
[MATHEMATICAL SUBJECT CODES] 54C30 (1)
[MATHEMATICAL SUBJECT CODES] 54C35 (1)
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